Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks

TL;DR

This paper reviews antiferromagnetic Heisenberg spin chains, highlighting hidden symmetries, and discusses recent advances using Conformal Field Theory and numerical methods to classify phases.

Contribution

It introduces a combined approach of Conformal Field Theory and numerical techniques to analyze phase classification in low-dimensional spin systems.

Findings

Identification of hidden symmetries in spin chains

Application of Conformal Field Theory to classify phases

Numerical validation using Density Matrix Renormalization Group

Abstract

We review here some general properties of antiferromagnetic Heisenberg spin chains, emphasizing and discussing the role of hidden symmetries in the classification of the various phases of the models. We present also some recent results that have been obtained with a combined use of Conformal Field Theory and of numerical Density Matrix Renormalization Group techniques.